Recent works such as [1]} and [2]} introduce the concepts of relative-smoothness, relative strong convexity and \(c\) -stability. These are weaker conditions than assumed in this paper. With these conditions, the proof techniques used to analyze coordinate descent algorithms are applicable to Newton-like algorithms, where instead of a fixed matrix \(\) , the actual Hessian \((x)\)  can be used. The extension to \(c-\) stability is done trivially in Theorem 2 of [2]}, here we focus on a slightly more elaborate connection with relative smoothness and relative strong-convexity.
